jessimm 發表於 17-10-20 20:09 
就係咁入左劍橋. 有些事情,當所有人都話無可能, 原來並不是咁神奇 數學嘅嘢，唔會咁神化，我係維基揾到以下內容，大家參考吓！
A summation method that is linear and stable cannot sum the series 1 + 2 + 3 + ⋯ to any finite value. (Stable means that adding a term to the beginning of the series increases the sum by the same amount.) This can be seen as follows. If 1 + 2 + 3 + ⋯ = xthen adding 0 to both sides gives 0 + 1 + 2 + ⋯ = 0 + x = x by stability.By linearity, one may subtract the second equation from the first (subtracting each component of the second line from the first line in columns) to give 1 + 1 + 1 + ⋯ = x – x = 0.Adding 0 to both sides again gives 0 + 1 + 1 + 1 + ⋯ = 0,and subtracting the last two series gives 1 + 0 + 0 + ⋯ = 0contradicting stability. The methods used above to sum 1 + 2 + 3 + ⋯ are either not stable or not linear. | 
發表於 17-10-22 17:39
